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A064771
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Let S(n) = set of divisors of n, excluding n; sequence gives n such that there is a unique subset of S(n) that sums to n.
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7
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6, 20, 28, 78, 88, 102, 104, 114, 138, 174, 186, 222, 246, 258, 272, 282, 304, 318, 354, 366, 368, 402, 426, 438, 464, 474, 490, 496, 498, 534, 572, 582, 606, 618, 642, 650, 654, 678, 748, 762, 786, 822, 834, 860, 894, 906, 940, 942, 978, 1002, 1014, 1038
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Perfect numbers (A000396) are a proper subset of this sequence. Weird numbers (A006037) are numbers whose proper divisors sum to more than the number, but no subset sums to the number.
Odd elements are rare: the first few are 8925, 32445, 351351, 442365; there are no more below 100 million. See A065235 for more details.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..200
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EXAMPLE
| Proper divisors of 20 are 1, 2, 4, 5 and 10. {1,4,5,10} is the only subset that sums to 20, so 20 is in the sequence.
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MATHEMATICA
| okQ[n_]:= Module[{d=Most[Divisors[n]]}, SeriesCoefficient[Series[Product[1+x^i, {i, d}], {x, 0, n}], n] == 1];
Select[Range[1100], okQ] [by Harvey P. Dale, Dec. 13, 2010
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CROSSREFS
| A005835 gives n such that some subset of S(n) sums to n. Cf. A065205.
Cf. A000396, A006037, A065205, A065235.
Sequence in context: A119425 A006039 A180332 * A006036 A140738 A031005
Adjacent sequences: A064768 A064769 A064770 * A064772 A064773 A064774
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 19 2001
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EXTENSIONS
| More terms from Don Reble (djr(AT)nk.ca), Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu) and Naohiro Nomoto (n_nomoto(AT)yabumi.com), Oct 22 2001
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